The transformation method is a powerful tool providing the constitutive parameters necessary for arbitrary geometric transformations of solution fields. These constitutive parameters, in elasticity, describe a constitutive law that, unlike conventional Hooke's law, is polar and chiral and that no known solids exhibit. This raises the question of whether polar and chiral elastic solids can be designed from the bottom up as architected lattice-based materials; this design task is a major challenge in the field of transformation elasticity. The present study aims to provide a theoretically justified design methodology based on a discrete transformation method. The key idea is to let the gradient of the geometric transformation operate not only on the elastic properties but on the underlying lattice-based architecture of the solids. As an outstanding application, we leverage the proposed design paradigm to construct a polar lattice metamaterial subsequently used for elastic carpet cloaking purposes. Numerical simulations are carried to show excellent cloaking performance under different static and dynamic mechanical loads and thus demonstrate the validity of the proposed designs. The approach presented herein could promote and accelerate new designs of lattice topologies for transformation elasticity in particular and can be extended to realize other emergent elastic properties and to unlock peculiar field-warping functions other than cloaking in static and dynamic contexts.

变换方法是提供解域任意几何变换所需的本构参数的强大工具。这些本构参数在弹性方面描述了一个本构定律，与传统的胡克定律不同，它是极性和手性的，并且没有已知的固体表现出来。这就提出了一个问题，即极性和手性弹性固体是否可以自下而上设计为基于晶格的结构材料？这个设计任务是变换弹性领域的一大挑战。本研究旨在提供一种基于离散变换方法的理论上合理的设计方法。关键思想是让几何变换的梯度不仅对弹性属性起作用，而且对固体的底层基于晶格的结构起作用。作为一项出色的应用，我们利用所提出的设计范式构建了一种极性晶格超材料，随后用于弹性地毯隐形。进行数值模拟以显示在不同静态和动态机械载荷下的出色隐形性能，从而证明了所提出设计的有效性。本文提出的方法可以促进和加速特别是用于变换弹性的晶格拓扑的新设计，并且可以扩展以实现其他紧急弹性特性，并解锁除静态和动态环境中的隐形之外的特殊场扭曲功能。进行数值模拟以显示在不同静态和动态机械载荷下的出色隐形性能，从而证明了所提出设计的有效性。本文提出的方法可以促进和加速特别是用于变换弹性的晶格拓扑的新设计，并且可以扩展以实现其他紧急弹性特性，并解锁除静态和动态环境中的隐形之外的特殊场扭曲功能。进行数值模拟以显示在不同静态和动态机械载荷下的出色隐形性能，从而证明了所提出设计的有效性。本文提出的方法可以促进和加速特别是用于变换弹性的晶格拓扑的新设计，并且可以扩展以实现其他紧急弹性特性，并解锁除静态和动态环境中的隐形之外的特殊场扭曲功能。